Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 2 5.622928
beta0_black 2 2.984519
beta0_yellow 1 1.999360
beta3_black 2 1.890653
beta1_yellow 3 1.556719
beta2_pH 7 1.553654
beta3_yellow 3 1.503963
beta2_yellow 3 1.503840
parameter n badRhat_avg
sd_comp 1 1.476180
beta2_pelagic 5 1.337625
beta2_black 2 1.326814
beta0_pelagic 2 1.324719
beta1_pelagic 6 1.255421
beta1_pH 12 1.211064
beta0_pH 2 1.206982
tau_beta0_yellow 2 1.199757
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
beta0_pelagic 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta0_pH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta0_yellow 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
beta1_black 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
beta1_pelagic 1 1 0 0 0 0 0 1 0 0 0 0 1 0 1 1
beta1_pH 1 1 1 0 1 0 1 0 0 0 0 1 1 0 0 1
beta1_yellow 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta2_black 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 0 0 1 0 0 1 0 0 0 1 1 0
beta2_pH 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1
beta2_yellow 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1
beta3_black 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
beta3_yellow 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.127 0.072 -0.262 -0.129 0.031
mu_bc_H[2] -0.095 0.044 -0.172 -0.098 -0.002
mu_bc_H[3] -0.435 0.070 -0.569 -0.435 -0.293
mu_bc_H[4] -0.984 0.195 -1.391 -0.981 -0.614
mu_bc_H[5] 0.938 0.964 -0.164 0.736 3.282
mu_bc_H[6] -2.155 0.326 -2.800 -2.161 -1.497
mu_bc_H[7] -0.455 0.110 -0.683 -0.452 -0.249
mu_bc_H[8] 0.238 0.353 -0.346 0.205 1.014
mu_bc_H[9] -0.289 0.136 -0.564 -0.289 -0.020
mu_bc_H[10] -0.107 0.070 -0.239 -0.108 0.034
mu_bc_H[11] -0.125 0.038 -0.200 -0.125 -0.051
mu_bc_H[12] -0.253 0.105 -0.485 -0.248 -0.057
mu_bc_H[13] -0.133 0.078 -0.281 -0.134 0.022
mu_bc_H[14] -0.304 0.098 -0.505 -0.301 -0.120
mu_bc_H[15] -0.342 0.050 -0.438 -0.344 -0.242
mu_bc_H[16] -0.272 0.387 -0.914 -0.297 0.547
mu_bc_R[1] 1.298 0.144 1.026 1.291 1.584
mu_bc_R[2] 1.453 0.093 1.269 1.453 1.632
mu_bc_R[3] 1.391 0.142 1.108 1.391 1.661
mu_bc_R[4] 0.903 0.203 0.468 0.915 1.272
mu_bc_R[5] 1.173 0.457 0.276 1.177 2.064
mu_bc_R[6] -1.587 0.430 -2.444 -1.584 -0.735
mu_bc_R[7] 0.335 0.197 -0.046 0.333 0.721
mu_bc_R[8] 0.552 0.195 0.164 0.557 0.923
mu_bc_R[9] 0.320 0.208 -0.131 0.337 0.690
mu_bc_R[10] 1.300 0.139 1.007 1.309 1.551
mu_bc_R[11] 1.040 0.097 0.852 1.039 1.221
mu_bc_R[12] 0.826 0.210 0.376 0.833 1.217
mu_bc_R[13] 1.025 0.103 0.823 1.025 1.227
mu_bc_R[14] 0.899 0.141 0.626 0.898 1.174
mu_bc_R[15] 0.778 0.111 0.560 0.779 0.998
mu_bc_R[16] 1.086 0.128 0.839 1.087 1.336
tau_pH[1] 5.303 0.447 4.452 5.284 6.218
tau_pH[2] 2.232 0.259 1.768 2.215 2.772
tau_pH[3] 2.251 0.223 1.849 2.240 2.704
beta0_pH[1,1] 0.525 0.173 0.175 0.531 0.850
beta0_pH[2,1] 1.336 0.178 0.976 1.339 1.679
beta0_pH[3,1] 1.388 0.205 0.941 1.407 1.719
beta0_pH[4,1] 1.554 0.216 1.065 1.577 1.929
beta0_pH[5,1] -0.856 0.282 -1.464 -0.840 -0.351
beta0_pH[6,1] -0.638 0.460 -1.774 -0.554 -0.005
beta0_pH[7,1] 0.233 0.664 -1.109 0.580 0.963
beta0_pH[8,1] -0.655 0.273 -1.239 -0.636 -0.194
beta0_pH[9,1] -0.627 0.281 -1.247 -0.610 -0.122
beta0_pH[10,1] 0.239 0.204 -0.179 0.243 0.627
beta0_pH[11,1] -0.086 0.171 -0.437 -0.081 0.230
beta0_pH[12,1] 0.498 0.185 0.125 0.502 0.852
beta0_pH[13,1] 0.014 0.142 -0.261 0.014 0.296
beta0_pH[14,1] -0.319 0.166 -0.663 -0.317 -0.006
beta0_pH[15,1] -0.023 0.179 -0.380 -0.014 0.323
beta0_pH[16,1] -0.573 0.473 -1.928 -0.465 0.034
beta0_pH[1,2] 2.797 0.169 2.460 2.803 3.119
beta0_pH[2,2] 2.861 0.139 2.589 2.860 3.129
beta0_pH[3,2] 2.816 0.380 2.016 2.907 3.356
beta0_pH[4,2] 2.869 0.205 2.297 2.893 3.171
beta0_pH[5,2] 4.643 1.344 2.937 4.372 8.125
beta0_pH[6,2] 3.063 0.244 2.547 3.076 3.500
beta0_pH[7,2] 1.960 0.169 1.622 1.962 2.294
beta0_pH[8,2] 2.858 0.194 2.519 2.861 3.187
beta0_pH[9,2] 3.335 0.362 2.241 3.384 3.814
beta0_pH[10,2] 3.714 0.203 3.323 3.714 4.099
beta0_pH[11,2] -4.855 0.296 -5.423 -4.846 -4.280
beta0_pH[12,2] -4.805 0.414 -5.672 -4.783 -4.021
beta0_pH[13,2] -4.592 0.398 -5.381 -4.597 -3.795
beta0_pH[14,2] -5.685 0.486 -6.683 -5.677 -4.806
beta0_pH[15,2] -4.275 0.336 -4.921 -4.271 -3.620
beta0_pH[16,2] -4.894 0.393 -5.721 -4.886 -4.149
beta0_pH[1,3] 0.627 0.557 -0.679 0.740 1.420
beta0_pH[2,3] 2.047 0.301 1.308 2.109 2.457
beta0_pH[3,3] 2.281 0.341 1.462 2.371 2.741
beta0_pH[4,3] 2.800 0.379 1.664 2.888 3.231
beta0_pH[5,3] 1.048 1.885 -2.183 0.839 5.406
beta0_pH[6,3] -0.715 1.119 -3.017 -0.809 1.414
beta0_pH[7,3] -2.152 0.656 -3.692 -2.081 -1.046
beta0_pH[8,3] 0.256 0.196 -0.131 0.258 0.642
beta0_pH[9,3] -1.180 0.815 -3.064 -0.926 -0.116
beta0_pH[10,3] -0.434 1.029 -2.623 -0.278 1.026
beta0_pH[11,3] -0.159 0.320 -0.777 -0.165 0.493
beta0_pH[12,3] -0.847 0.356 -1.608 -0.821 -0.215
beta0_pH[13,3] -0.110 0.312 -0.706 -0.118 0.528
beta0_pH[14,3] -0.265 0.262 -0.771 -0.265 0.259
beta0_pH[15,3] -0.710 0.307 -1.332 -0.697 -0.141
beta0_pH[16,3] -0.384 0.286 -0.951 -0.381 0.189
beta1_pH[1,1] 3.114 0.306 2.566 3.094 3.758
beta1_pH[2,1] 2.222 0.342 1.721 2.189 2.898
beta1_pH[3,1] 2.047 0.319 1.530 2.018 2.759
beta1_pH[4,1] 2.418 0.348 1.877 2.373 3.246
beta1_pH[5,1] 2.286 0.343 1.704 2.256 3.055
beta1_pH[6,1] 3.866 1.100 2.294 3.643 6.483
beta1_pH[7,1] 2.564 1.736 0.413 2.352 6.657
beta1_pH[8,1] 4.004 0.940 2.642 3.840 6.301
beta1_pH[9,1] 2.308 0.424 1.671 2.263 3.190
beta1_pH[10,1] 2.382 0.285 1.848 2.370 2.974
beta1_pH[11,1] 3.275 0.211 2.876 3.270 3.708
beta1_pH[12,1] 2.536 0.216 2.109 2.534 2.959
beta1_pH[13,1] 2.968 0.212 2.570 2.963 3.388
beta1_pH[14,1] 3.431 0.213 3.031 3.430 3.863
beta1_pH[15,1] 2.526 0.226 2.095 2.522 2.994
beta1_pH[16,1] 4.297 0.802 3.228 4.117 6.496
beta1_pH[1,2] 0.076 0.725 0.000 0.000 0.612
beta1_pH[2,2] 0.185 2.548 0.000 0.000 0.471
beta1_pH[3,2] 0.554 0.709 0.000 0.065 1.672
beta1_pH[4,2] 0.294 1.922 0.000 0.000 2.032
beta1_pH[5,2] 0.146 0.873 0.000 0.001 1.989
beta1_pH[6,2] 0.334 1.847 0.000 0.001 2.227
beta1_pH[7,2] 0.219 1.407 0.000 0.001 1.122
beta1_pH[8,2] 0.040 0.306 0.000 0.001 0.298
beta1_pH[9,2] 0.237 2.316 0.000 0.001 1.744
beta1_pH[10,2] 9.267 25.924 0.000 0.002 105.937
beta1_pH[11,2] 6.699 0.328 6.069 6.703 7.351
beta1_pH[12,2] 6.529 0.501 5.612 6.499 7.615
beta1_pH[13,2] 7.003 0.439 6.136 7.016 7.856
beta1_pH[14,2] 7.345 0.502 6.417 7.328 8.376
beta1_pH[15,2] 6.772 0.362 6.029 6.775 7.472
beta1_pH[16,2] 7.512 0.427 6.676 7.501 8.387
beta1_pH[1,3] 2.905 1.123 1.525 2.608 5.984
beta1_pH[2,3] 1.969 9.616 0.000 0.262 8.855
beta1_pH[3,3] 0.769 1.729 0.000 0.267 5.675
beta1_pH[4,3] 0.892 2.775 0.000 0.157 5.706
beta1_pH[5,3] 6.130 7.668 1.612 3.502 33.198
beta1_pH[6,3] 2.706 1.562 0.818 2.607 4.990
beta1_pH[7,3] 3.019 0.663 1.941 2.947 4.574
beta1_pH[8,3] 2.840 0.374 2.120 2.831 3.578
beta1_pH[9,3] 3.252 0.822 2.112 3.057 5.147
beta1_pH[10,3] 3.868 1.114 2.268 3.674 6.291
beta1_pH[11,3] 2.745 0.383 2.006 2.740 3.537
beta1_pH[12,3] 4.088 0.451 3.276 4.069 5.011
beta1_pH[13,3] 1.693 0.333 1.020 1.698 2.314
beta1_pH[14,3] 2.489 0.328 1.851 2.485 3.145
beta1_pH[15,3] 1.987 0.328 1.388 1.975 2.637
beta1_pH[16,3] 1.783 0.317 1.146 1.787 2.388
beta2_pH[1,1] 0.466 0.113 0.293 0.452 0.729
beta2_pH[2,1] 0.536 0.247 0.227 0.490 1.114
beta2_pH[3,1] 0.587 0.367 0.208 0.514 1.494
beta2_pH[4,1] 0.458 0.176 0.203 0.430 0.866
beta2_pH[5,1] 1.548 1.281 0.245 1.256 5.029
beta2_pH[6,1] 0.187 0.069 0.090 0.176 0.357
beta2_pH[7,1] -0.789 1.721 -5.240 0.015 1.340
beta2_pH[8,1] 0.246 0.104 0.135 0.226 0.476
beta2_pH[9,1] 0.441 0.218 0.180 0.399 0.928
beta2_pH[10,1] 0.623 0.305 0.290 0.560 1.323
beta2_pH[11,1] 0.784 0.210 0.475 0.751 1.294
beta2_pH[12,1] 1.363 0.478 0.741 1.259 2.574
beta2_pH[13,1] 0.737 0.214 0.411 0.707 1.252
beta2_pH[14,1] 0.824 0.197 0.532 0.790 1.294
beta2_pH[15,1] 0.800 0.287 0.401 0.744 1.549
beta2_pH[16,1] 0.344 0.161 0.145 0.303 0.783
beta2_pH[1,2] -1.951 4.198 -10.071 -1.997 6.360
beta2_pH[2,2] -2.040 4.160 -10.600 -2.047 6.658
beta2_pH[3,2] -2.444 3.928 -9.831 -2.498 6.458
beta2_pH[4,2] -2.135 4.081 -9.963 -2.178 6.410
beta2_pH[5,2] -0.807 4.101 -8.699 -0.970 7.221
beta2_pH[6,2] -0.912 4.234 -8.966 -1.041 7.742
beta2_pH[7,2] -0.858 4.142 -8.857 -1.050 7.625
beta2_pH[8,2] -0.838 4.238 -8.826 -1.060 7.942
beta2_pH[9,2] -0.933 4.315 -9.178 -1.199 7.916
beta2_pH[10,2] -1.286 4.413 -9.737 -1.558 7.978
beta2_pH[11,2] -7.118 2.425 -12.900 -6.713 -3.644
beta2_pH[12,2] -4.357 2.693 -10.450 -4.077 -0.752
beta2_pH[13,2] -4.485 2.397 -10.308 -3.942 -1.464
beta2_pH[14,2] -5.329 2.184 -10.612 -4.996 -2.151
beta2_pH[15,2] -6.949 2.575 -13.195 -6.427 -3.397
beta2_pH[16,2] -7.190 2.674 -14.153 -6.617 -3.656
beta2_pH[1,3] 1.743 2.172 0.136 0.589 7.465
beta2_pH[2,3] 0.500 3.932 -7.662 0.515 8.927
beta2_pH[3,3] -0.496 3.951 -8.293 -0.703 7.782
beta2_pH[4,3] 0.381 3.696 -6.960 0.221 7.552
beta2_pH[5,3] 3.347 2.985 -0.166 2.668 10.665
beta2_pH[6,3] 3.366 3.024 -0.473 2.809 10.609
beta2_pH[7,3] 3.352 2.672 0.495 2.586 10.176
beta2_pH[8,3] 4.714 2.899 0.739 4.278 11.396
beta2_pH[9,3] 2.661 2.744 0.281 1.418 9.544
beta2_pH[10,3] 1.951 2.434 0.289 0.692 8.893
beta2_pH[11,3] -2.581 2.320 -9.564 -1.787 -0.605
beta2_pH[12,3] -2.837 2.286 -10.216 -2.011 -0.949
beta2_pH[13,3] -3.635 2.712 -10.885 -2.686 -0.854
beta2_pH[14,3] -3.544 2.655 -10.679 -2.572 -0.932
beta2_pH[15,3] -4.943 3.597 -11.557 -3.250 -1.058
beta2_pH[16,3] -3.795 2.784 -11.071 -2.766 -0.881
beta3_pH[1,1] 35.872 0.825 34.266 35.857 37.530
beta3_pH[2,1] 33.595 1.492 31.430 33.423 36.758
beta3_pH[3,1] 33.705 1.099 31.601 33.696 35.924
beta3_pH[4,1] 33.835 1.211 31.691 33.755 36.337
beta3_pH[5,1] 27.830 1.218 26.456 27.511 31.372
beta3_pH[6,1] 38.945 3.152 33.124 38.795 45.148
beta3_pH[7,1] 27.673 9.594 18.249 22.218 45.653
beta3_pH[8,1] 39.998 2.071 36.153 39.842 44.684
beta3_pH[9,1] 30.707 1.621 28.068 30.577 33.914
beta3_pH[10,1] 32.703 0.899 31.069 32.657 34.596
beta3_pH[11,1] 30.400 0.455 29.470 30.412 31.264
beta3_pH[12,1] 30.195 0.394 29.417 30.203 30.941
beta3_pH[13,1] 33.227 0.595 32.157 33.224 34.491
beta3_pH[14,1] 32.074 0.446 31.193 32.073 32.924
beta3_pH[15,1] 31.247 0.644 29.987 31.227 32.550
beta3_pH[16,1] 32.081 1.040 30.065 32.020 34.250
beta3_pH[1,2] 30.010 8.012 18.429 28.942 44.950
beta3_pH[2,2] 29.781 8.029 18.461 28.631 44.778
beta3_pH[3,2] 35.253 8.435 18.781 40.323 44.279
beta3_pH[4,2] 30.700 8.205 18.464 29.646 45.055
beta3_pH[5,2] 30.093 8.012 18.437 29.160 44.888
beta3_pH[6,2] 30.706 7.842 18.543 30.721 44.810
beta3_pH[7,2] 29.699 8.067 18.481 28.669 44.820
beta3_pH[8,2] 29.978 8.081 18.424 29.123 44.941
beta3_pH[9,2] 30.915 8.588 18.424 29.798 45.339
beta3_pH[10,2] 29.376 6.935 18.530 28.991 44.124
beta3_pH[11,2] 43.397 0.157 43.144 43.383 43.738
beta3_pH[12,2] 43.186 0.205 42.733 43.175 43.620
beta3_pH[13,2] 43.827 0.154 43.477 43.853 44.069
beta3_pH[14,2] 43.331 0.169 43.082 43.308 43.731
beta3_pH[15,2] 43.401 0.165 43.138 43.379 43.759
beta3_pH[16,2] 43.498 0.166 43.199 43.492 43.820
beta3_pH[1,3] 38.903 2.127 34.456 39.439 42.941
beta3_pH[2,3] 29.565 7.996 18.393 28.381 44.786
beta3_pH[3,3] 31.780 8.891 18.516 31.504 44.376
beta3_pH[4,3] 28.378 7.805 18.291 26.418 44.925
beta3_pH[5,3] 26.108 6.574 18.295 24.394 41.919
beta3_pH[6,3] 27.062 6.233 18.605 25.719 44.314
beta3_pH[7,3] 26.587 1.006 24.886 26.454 28.875
beta3_pH[8,3] 41.495 0.375 40.809 41.488 42.186
beta3_pH[9,3] 32.089 1.959 27.336 32.983 34.164
beta3_pH[10,3] 34.450 1.587 31.269 34.554 36.707
beta3_pH[11,3] 41.759 0.805 40.122 41.804 43.214
beta3_pH[12,3] 41.721 0.384 40.963 41.741 42.481
beta3_pH[13,3] 42.707 0.853 41.021 42.769 44.517
beta3_pH[14,3] 41.120 0.558 39.924 41.153 42.115
beta3_pH[15,3] 42.729 0.676 41.198 42.868 43.757
beta3_pH[16,3] 42.949 0.724 41.275 43.076 44.067
beta0_pelagic[1] 1.980 0.374 1.013 2.099 2.416
beta0_pelagic[2] 1.334 0.323 0.471 1.426 1.720
beta0_pelagic[3] 0.206 0.364 -0.788 0.259 0.764
beta0_pelagic[4] 0.275 0.385 -0.551 0.294 0.982
beta0_pelagic[5] 1.122 0.382 0.710 1.155 1.518
beta0_pelagic[6] 1.440 0.195 1.036 1.455 1.736
beta0_pelagic[7] 1.612 0.141 1.333 1.612 1.886
beta0_pelagic[8] 1.731 0.141 1.468 1.733 1.995
beta0_pelagic[9] 2.564 0.404 1.275 2.666 2.987
beta0_pelagic[10] 2.559 0.130 2.296 2.561 2.817
beta0_pelagic[11] -0.039 0.470 -1.064 0.031 0.634
beta0_pelagic[12] 1.684 0.143 1.402 1.686 1.963
beta0_pelagic[13] 0.321 0.195 -0.084 0.331 0.663
beta0_pelagic[14] -0.147 0.286 -0.807 -0.120 0.345
beta0_pelagic[15] -0.276 0.133 -0.539 -0.276 -0.022
beta0_pelagic[16] 0.137 0.336 -0.628 0.195 0.611
beta1_pelagic[1] 0.284 0.411 0.000 0.083 1.354
beta1_pelagic[2] 0.253 0.372 0.000 0.075 1.142
beta1_pelagic[3] 0.883 0.469 0.170 0.805 2.287
beta1_pelagic[4] 0.914 0.423 0.007 0.891 1.872
beta1_pelagic[5] 0.046 0.366 0.000 0.000 0.059
beta1_pelagic[6] 0.040 0.205 0.000 0.000 0.661
beta1_pelagic[7] 0.053 0.414 0.000 0.000 0.200
beta1_pelagic[8] 0.010 0.096 0.000 0.000 0.042
beta1_pelagic[9] 0.197 0.661 0.000 0.000 1.792
beta1_pelagic[10] 0.016 0.179 0.000 0.000 0.086
beta1_pelagic[11] 3.890 1.007 2.256 3.800 5.997
beta1_pelagic[12] 2.825 0.313 2.237 2.814 3.420
beta1_pelagic[13] 2.892 0.733 1.772 2.801 4.548
beta1_pelagic[14] 4.584 1.087 2.970 4.410 6.855
beta1_pelagic[15] 2.941 0.272 2.416 2.946 3.470
beta1_pelagic[16] 4.158 1.125 2.752 3.801 6.798
beta2_pelagic[1] 1.451 2.515 -3.873 1.190 7.125
beta2_pelagic[2] 1.353 2.034 -2.633 1.018 6.562
beta2_pelagic[3] 1.566 1.574 0.104 1.010 5.631
beta2_pelagic[4] 1.659 1.344 0.162 1.471 5.354
beta2_pelagic[5] -0.063 2.890 -6.225 -0.053 6.499
beta2_pelagic[6] 0.340 2.793 -5.624 0.205 6.633
beta2_pelagic[7] -0.030 2.727 -5.853 -0.019 6.043
beta2_pelagic[8] 0.048 2.926 -6.477 0.039 6.454
beta2_pelagic[9] 0.272 2.863 -5.936 0.269 6.303
beta2_pelagic[10] 0.021 2.824 -5.939 0.007 6.207
beta2_pelagic[11] 0.581 1.037 0.121 0.229 3.877
beta2_pelagic[12] 3.913 2.344 1.011 3.389 10.175
beta2_pelagic[13] 0.718 0.774 0.197 0.478 2.900
beta2_pelagic[14] 0.298 0.211 0.151 0.270 0.601
beta2_pelagic[15] 3.816 2.037 1.218 3.210 9.282
beta2_pelagic[16] 1.628 2.253 0.172 0.455 8.017
beta3_pelagic[1] 27.974 7.800 18.456 25.280 44.903
beta3_pelagic[2] 29.058 8.397 18.305 26.783 45.277
beta3_pelagic[3] 30.139 4.511 22.447 29.889 41.824
beta3_pelagic[4] 25.978 3.459 20.942 25.586 37.311
beta3_pelagic[5] 30.110 8.017 18.519 29.290 45.354
beta3_pelagic[6] 30.030 7.656 18.571 29.324 44.723
beta3_pelagic[7] 29.907 8.121 18.483 28.815 45.143
beta3_pelagic[8] 29.766 7.969 18.457 28.708 44.946
beta3_pelagic[9] 29.918 7.538 18.585 28.861 44.388
beta3_pelagic[10] 29.860 8.083 18.446 28.642 44.941
beta3_pelagic[11] 41.919 2.603 35.194 42.633 45.736
beta3_pelagic[12] 43.456 0.272 42.978 43.441 43.959
beta3_pelagic[13] 42.796 1.301 40.382 42.740 45.456
beta3_pelagic[14] 42.586 1.728 39.049 42.562 45.717
beta3_pelagic[15] 43.115 0.251 42.515 43.135 43.569
beta3_pelagic[16] 43.020 1.116 40.508 43.116 45.430
mu_beta0_pelagic[1] 0.896 0.815 -0.838 0.896 2.526
mu_beta0_pelagic[2] 1.810 0.418 0.933 1.818 2.616
mu_beta0_pelagic[3] 0.278 0.475 -0.664 0.287 1.183
tau_beta0_pelagic[1] 1.264 2.618 0.063 0.676 5.786
tau_beta0_pelagic[2] 2.194 1.832 0.218 1.721 6.651
tau_beta0_pelagic[3] 1.453 1.083 0.160 1.179 4.279
beta0_yellow[1] -0.552 0.203 -1.018 -0.528 -0.233
beta0_yellow[2] 0.488 0.182 0.087 0.502 0.789
beta0_yellow[3] -0.314 0.200 -0.765 -0.305 0.063
beta0_yellow[4] 0.795 0.304 -0.023 0.851 1.205
beta0_yellow[5] -0.973 0.541 -1.979 -0.983 0.019
beta0_yellow[6] 0.290 0.220 -0.137 0.295 0.714
beta0_yellow[7] 1.017 0.249 0.667 1.036 1.351
beta0_yellow[8] 0.774 0.563 -0.998 0.940 1.280
beta0_yellow[9] -0.058 0.350 -0.632 -0.067 0.655
beta0_yellow[10] 0.238 0.152 -0.065 0.237 0.528
beta0_yellow[11] -2.021 0.453 -2.970 -2.000 -1.199
beta0_yellow[12] -3.645 0.420 -4.507 -3.622 -2.896
beta0_yellow[13] -3.737 0.459 -4.688 -3.718 -2.906
beta0_yellow[14] -2.182 0.486 -3.107 -2.183 -1.210
beta0_yellow[15] -2.917 0.445 -3.806 -2.892 -2.081
beta0_yellow[16] -2.447 0.455 -3.337 -2.431 -1.549
beta1_yellow[1] 0.493 0.566 0.000 0.325 2.003
beta1_yellow[2] 1.124 0.454 0.576 1.047 2.442
beta1_yellow[3] 0.699 0.332 0.025 0.680 1.485
beta1_yellow[4] 1.496 0.832 0.657 1.247 4.069
beta1_yellow[5] 2.124 2.110 0.000 2.335 5.312
beta1_yellow[6] 2.257 0.365 1.539 2.252 2.981
beta1_yellow[7] 4.287 6.029 0.000 2.980 17.286
beta1_yellow[8] 1.593 2.402 0.000 0.984 7.321
beta1_yellow[9] 1.559 0.649 0.536 1.519 2.873
beta1_yellow[10] 2.356 0.485 1.466 2.328 3.362
beta1_yellow[11] 2.175 0.448 1.354 2.145 3.117
beta1_yellow[12] 2.452 0.430 1.685 2.432 3.353
beta1_yellow[13] 2.855 0.462 2.047 2.829 3.812
beta1_yellow[14] 2.250 0.483 1.277 2.247 3.192
beta1_yellow[15] 2.159 0.443 1.314 2.143 3.070
beta1_yellow[16] 2.205 0.449 1.326 2.201 3.125
beta2_yellow[1] -2.350 2.886 -9.169 -1.683 2.467
beta2_yellow[2] -2.656 2.489 -9.003 -1.807 -0.142
beta2_yellow[3] -2.308 2.445 -8.890 -1.384 -0.095
beta2_yellow[4] -2.241 2.522 -8.799 -1.218 -0.088
beta2_yellow[5] -2.808 4.121 -10.950 -2.862 6.883
beta2_yellow[6] 3.688 2.356 0.918 3.086 9.796
beta2_yellow[7] -2.793 4.302 -10.629 -3.180 7.024
beta2_yellow[8] -1.209 4.373 -10.072 -1.166 7.915
beta2_yellow[9] 3.572 2.794 -0.702 3.229 9.803
beta2_yellow[10] -3.961 2.485 -9.895 -3.517 -0.687
beta2_yellow[11] -4.184 2.504 -11.048 -3.561 -1.162
beta2_yellow[12] -4.309 2.318 -10.140 -3.790 -1.260
beta2_yellow[13] -4.182 2.194 -9.915 -3.630 -1.470
beta2_yellow[14] -4.312 2.441 -10.617 -3.837 -0.951
beta2_yellow[15] -3.880 2.158 -9.318 -3.396 -1.165
beta2_yellow[16] -4.319 2.339 -10.608 -3.799 -1.352
beta3_yellow[1] 27.340 7.705 18.321 24.640 44.425
beta3_yellow[2] 29.061 2.131 23.547 28.947 32.892
beta3_yellow[3] 32.672 3.795 22.224 32.817 40.348
beta3_yellow[4] 29.058 3.668 20.920 28.139 36.031
beta3_yellow[5] 32.427 4.875 19.493 33.293 42.752
beta3_yellow[6] 39.693 0.565 38.695 39.645 41.010
beta3_yellow[7] 23.460 6.694 18.500 20.328 42.808
beta3_yellow[8] 26.618 6.965 18.304 24.762 44.119
beta3_yellow[9] 37.348 3.309 23.935 37.568 42.892
beta3_yellow[10] 29.294 0.655 27.600 29.401 30.191
beta3_yellow[11] 45.343 0.500 44.123 45.449 45.976
beta3_yellow[12] 43.339 0.425 42.501 43.303 44.204
beta3_yellow[13] 44.855 0.379 44.014 44.921 45.507
beta3_yellow[14] 44.320 0.947 43.160 44.302 45.847
beta3_yellow[15] 45.218 0.527 44.143 45.234 45.971
beta3_yellow[16] 44.622 0.638 43.426 44.619 45.842
mu_beta0_yellow[1] 0.093 0.554 -1.000 0.085 1.259
mu_beta0_yellow[2] 0.198 0.456 -0.766 0.212 1.066
mu_beta0_yellow[3] -2.501 0.601 -3.495 -2.569 -1.094
tau_beta0_yellow[1] 1.993 2.987 0.100 1.190 8.453
tau_beta0_yellow[2] 1.721 1.802 0.177 1.188 6.221
tau_beta0_yellow[3] 1.585 2.669 0.126 0.981 5.999
beta0_black[1] 0.102 0.194 -0.301 0.120 0.431
beta0_black[2] 1.913 0.127 1.665 1.912 2.166
beta0_black[3] 1.318 0.133 1.054 1.316 1.576
beta0_black[4] 2.433 0.135 2.162 2.436 2.683
beta0_black[5] 1.724 2.100 -2.833 1.704 6.295
beta0_black[6] 1.731 2.121 -3.084 1.754 6.007
beta0_black[7] 1.741 2.076 -2.691 1.739 6.152
beta0_black[8] 1.300 0.223 0.875 1.304 1.740
beta0_black[9] 2.441 0.246 1.962 2.447 2.914
beta0_black[10] 1.477 0.131 1.210 1.480 1.726
beta0_black[11] 3.490 0.149 3.200 3.491 3.780
beta0_black[12] 4.852 0.176 4.512 4.849 5.200
beta0_black[13] 0.244 0.500 -0.497 0.065 1.120
beta0_black[14] 2.855 0.158 2.540 2.860 3.152
beta0_black[15] 1.292 0.157 0.982 1.294 1.586
beta0_black[16] 4.274 0.155 3.970 4.274 4.576
beta2_black[1] 0.965 3.370 -5.986 1.113 7.841
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.516 2.632 -7.207 -1.437 4.727
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 33.653 8.595 18.640 35.497 44.413
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 36.133 6.367 19.385 39.075 42.461
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.281 0.193 -0.658 -0.285 0.095
beta4_black[2] 0.242 0.180 -0.111 0.241 0.585
beta4_black[3] -0.936 0.192 -1.318 -0.938 -0.556
beta4_black[4] 0.410 0.214 -0.009 0.402 0.829
beta4_black[5] 0.146 2.466 -4.821 0.140 5.030
beta4_black[6] 0.165 2.370 -4.584 0.143 5.020
beta4_black[7] 0.190 2.369 -4.581 0.111 5.331
beta4_black[8] -0.714 0.370 -1.448 -0.706 0.003
beta4_black[9] 1.460 1.019 -0.133 1.327 3.778
beta4_black[10] 0.025 0.183 -0.338 0.024 0.393
beta4_black[11] -0.698 0.213 -1.114 -0.698 -0.285
beta4_black[12] 0.169 0.328 -0.457 0.160 0.844
beta4_black[13] -1.181 0.218 -1.615 -1.182 -0.760
beta4_black[14] -0.187 0.233 -0.634 -0.188 0.277
beta4_black[15] -0.887 0.214 -1.302 -0.891 -0.471
beta4_black[16] -0.603 0.222 -1.044 -0.604 -0.175
mu_beta0_black[1] 1.469 0.931 -0.518 1.453 3.410
mu_beta0_black[2] 1.730 1.103 -0.651 1.733 4.083
mu_beta0_black[3] 2.816 0.999 0.780 2.820 4.839
tau_beta0_black[1] 0.706 0.693 0.055 0.487 2.593
tau_beta0_black[2] 2.016 4.149 0.053 0.815 10.737
tau_beta0_black[3] 0.265 0.185 0.050 0.218 0.725
beta0_dsr[11] -2.884 0.284 -3.438 -2.883 -2.322
beta0_dsr[12] 4.540 0.281 4.002 4.534 5.113
beta0_dsr[13] -1.331 0.297 -1.916 -1.326 -0.762
beta0_dsr[14] -3.650 0.502 -4.642 -3.648 -2.702
beta0_dsr[15] -1.927 0.282 -2.480 -1.925 -1.375
beta0_dsr[16] -2.984 0.361 -3.685 -2.979 -2.271
beta1_dsr[11] 4.820 0.300 4.228 4.826 5.392
beta1_dsr[12] 6.516 7.098 2.291 5.004 19.020
beta1_dsr[13] 2.844 0.314 2.231 2.836 3.449
beta1_dsr[14] 6.313 0.527 5.279 6.311 7.357
beta1_dsr[15] 3.326 0.283 2.784 3.330 3.873
beta1_dsr[16] 5.805 0.370 5.060 5.802 6.543
beta2_dsr[11] -8.220 2.235 -13.376 -7.896 -4.703
beta2_dsr[12] -7.134 2.613 -12.963 -6.946 -2.348
beta2_dsr[13] -6.585 2.641 -12.243 -6.514 -1.731
beta2_dsr[14] -6.212 2.637 -11.873 -6.102 -1.913
beta2_dsr[15] -7.836 2.437 -13.494 -7.503 -4.044
beta2_dsr[16] -7.954 2.202 -13.194 -7.705 -4.434
beta3_dsr[11] 43.486 0.151 43.213 43.485 43.771
beta3_dsr[12] 33.975 0.710 32.217 34.123 34.817
beta3_dsr[13] 43.240 0.288 42.831 43.185 43.856
beta3_dsr[14] 43.348 0.236 43.077 43.280 43.969
beta3_dsr[15] 43.510 0.185 43.172 43.510 43.856
beta3_dsr[16] 43.438 0.159 43.169 43.427 43.763
beta4_dsr[11] 0.577 0.215 0.163 0.578 0.999
beta4_dsr[12] 0.251 0.445 -0.626 0.242 1.175
beta4_dsr[13] -0.177 0.221 -0.603 -0.177 0.249
beta4_dsr[14] 0.146 0.252 -0.351 0.149 0.637
beta4_dsr[15] 0.720 0.216 0.307 0.722 1.153
beta4_dsr[16] 0.135 0.223 -0.315 0.138 0.567
beta0_slope[11] -1.939 0.162 -2.254 -1.938 -1.627
beta0_slope[12] -4.673 0.263 -5.200 -4.668 -4.171
beta0_slope[13] -1.338 0.221 -1.831 -1.323 -0.965
beta0_slope[14] -2.636 0.181 -2.992 -2.633 -2.285
beta0_slope[15] -1.371 0.167 -1.702 -1.376 -1.041
beta0_slope[16] -2.713 0.175 -3.045 -2.716 -2.366
beta1_slope[11] 4.591 0.297 4.013 4.594 5.176
beta1_slope[12] 4.989 0.515 3.978 4.985 6.039
beta1_slope[13] 2.951 0.567 2.251 2.864 4.714
beta1_slope[14] 6.549 0.568 5.463 6.535 7.704
beta1_slope[15] 3.059 0.288 2.508 3.059 3.623
beta1_slope[16] 5.358 0.399 4.588 5.354 6.153
beta2_slope[11] 7.962 2.351 4.446 7.585 13.331
beta2_slope[12] 7.094 2.511 2.782 6.851 13.016
beta2_slope[13] 5.651 2.985 0.360 5.766 11.660
beta2_slope[14] 6.483 2.364 2.489 6.331 11.661
beta2_slope[15] 7.496 2.428 3.733 7.169 13.146
beta2_slope[16] 7.612 2.341 3.858 7.273 13.014
beta3_slope[11] 43.471 0.153 43.199 43.463 43.770
beta3_slope[12] 43.420 0.231 43.066 43.393 43.900
beta3_slope[13] 43.657 0.470 42.917 43.727 44.525
beta3_slope[14] 43.322 0.172 43.090 43.284 43.758
beta3_slope[15] 43.511 0.196 43.150 43.508 43.872
beta3_slope[16] 43.461 0.168 43.171 43.453 43.794
beta4_slope[11] -0.578 0.213 -1.002 -0.576 -0.171
beta4_slope[12] -1.364 0.654 -2.886 -1.284 -0.307
beta4_slope[13] 0.044 0.225 -0.395 0.045 0.496
beta4_slope[14] -0.184 0.254 -0.670 -0.188 0.310
beta4_slope[15] -0.730 0.217 -1.163 -0.723 -0.319
beta4_slope[16] -0.207 0.236 -0.665 -0.204 0.252
sigma_H[1] 0.198 0.053 0.102 0.196 0.309
sigma_H[2] 0.171 0.031 0.118 0.168 0.235
sigma_H[3] 0.196 0.042 0.121 0.194 0.288
sigma_H[4] 0.419 0.078 0.295 0.410 0.586
sigma_H[5] 0.993 0.204 0.639 0.981 1.437
sigma_H[6] 0.397 0.205 0.037 0.390 0.819
sigma_H[7] 0.305 0.062 0.205 0.298 0.455
sigma_H[8] 0.414 0.086 0.273 0.405 0.610
sigma_H[9] 0.525 0.126 0.334 0.507 0.823
sigma_H[10] 0.216 0.043 0.143 0.213 0.310
sigma_H[11] 0.278 0.046 0.199 0.274 0.377
sigma_H[12] 0.437 0.165 0.211 0.411 0.768
sigma_H[13] 0.215 0.037 0.150 0.212 0.298
sigma_H[14] 0.510 0.094 0.343 0.505 0.708
sigma_H[15] 0.247 0.041 0.178 0.243 0.343
sigma_H[16] 0.223 0.043 0.153 0.219 0.319
lambda_H[1] 3.137 4.368 0.171 1.777 14.445
lambda_H[2] 8.173 7.420 0.763 5.980 28.398
lambda_H[3] 6.279 9.260 0.235 3.210 31.842
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.837 7.973 0.037 1.062 26.221
lambda_H[6] 7.993 15.712 0.008 1.154 50.738
lambda_H[7] 0.013 0.010 0.002 0.010 0.037
lambda_H[8] 8.675 11.265 0.151 4.930 39.855
lambda_H[9] 0.015 0.010 0.003 0.013 0.041
lambda_H[10] 0.341 1.332 0.032 0.198 1.165
lambda_H[11] 0.278 0.460 0.012 0.131 1.230
lambda_H[12] 5.004 6.852 0.207 2.878 22.985
lambda_H[13] 3.479 3.099 0.212 2.653 11.605
lambda_H[14] 3.307 4.164 0.229 1.965 14.096
lambda_H[15] 0.036 0.295 0.004 0.017 0.103
lambda_H[16] 0.791 1.077 0.041 0.414 3.991
mu_lambda_H[1] 4.398 1.905 1.237 4.240 8.652
mu_lambda_H[2] 3.862 1.931 0.601 3.740 7.928
mu_lambda_H[3] 3.540 1.858 0.834 3.252 7.849
sigma_lambda_H[1] 8.733 4.314 2.107 8.083 18.363
sigma_lambda_H[2] 8.396 4.597 0.975 7.934 18.153
sigma_lambda_H[3] 6.389 4.065 1.064 5.454 16.418
beta_H[1,1] 6.907 1.073 4.442 7.062 8.515
beta_H[2,1] 9.871 0.496 8.847 9.889 10.754
beta_H[3,1] 8.009 0.799 6.121 8.118 9.284
beta_H[4,1] 9.284 7.833 -7.264 9.455 23.902
beta_H[5,1] 0.170 2.241 -4.503 0.366 3.979
beta_H[6,1] 3.224 3.888 -6.896 4.632 7.665
beta_H[7,1] 0.259 5.917 -12.584 0.579 10.868
beta_H[8,1] 1.278 3.227 -2.421 1.280 3.461
beta_H[9,1] 13.124 5.774 1.381 13.142 24.660
beta_H[10,1] 7.111 1.711 3.540 7.148 10.470
beta_H[11,1] 5.213 3.469 -2.445 5.949 10.130
beta_H[12,1] 2.614 1.028 0.744 2.546 4.853
beta_H[13,1] 9.053 0.896 7.042 9.137 10.519
beta_H[14,1] 2.190 1.065 0.167 2.176 4.155
beta_H[15,1] -6.066 3.842 -12.827 -6.302 2.618
beta_H[16,1] 3.573 2.743 -0.973 3.206 9.879
beta_H[1,2] 7.902 0.250 7.395 7.915 8.363
beta_H[2,2] 10.024 0.135 9.761 10.023 10.295
beta_H[3,2] 8.960 0.200 8.573 8.956 9.366
beta_H[4,2] 3.569 1.472 0.862 3.493 6.612
beta_H[5,2] 1.941 0.936 0.012 1.974 3.684
beta_H[6,2] 5.767 1.031 3.293 5.964 7.361
beta_H[7,2] 2.672 1.127 0.718 2.608 5.101
beta_H[8,2] 3.039 0.981 1.392 3.160 4.269
beta_H[9,2] 3.493 1.122 1.415 3.479 5.852
beta_H[10,2] 8.188 0.346 7.449 8.197 8.820
beta_H[11,2] 9.758 0.633 8.821 9.639 11.188
beta_H[12,2] 3.956 0.372 3.276 3.936 4.745
beta_H[13,2] 9.122 0.253 8.668 9.111 9.646
beta_H[14,2] 4.029 0.348 3.382 4.020 4.734
beta_H[15,2] 11.355 0.678 9.893 11.401 12.615
beta_H[16,2] 4.546 0.818 2.972 4.536 6.169
beta_H[1,3] 8.459 0.238 8.029 8.444 8.958
beta_H[2,3] 10.065 0.117 9.839 10.061 10.302
beta_H[3,3] 9.621 0.160 9.311 9.614 9.951
beta_H[4,3] -2.535 0.869 -4.256 -2.511 -0.847
beta_H[5,3] 3.826 0.616 2.536 3.845 4.962
beta_H[6,3] 7.956 1.154 6.388 7.595 10.409
beta_H[7,3] -2.776 0.733 -4.245 -2.762 -1.325
beta_H[8,3] 5.249 0.453 4.654 5.195 6.157
beta_H[9,3] -2.858 0.744 -4.300 -2.842 -1.412
beta_H[10,3] 8.700 0.272 8.174 8.703 9.231
beta_H[11,3] 8.542 0.282 7.936 8.563 9.038
beta_H[12,3] 5.260 0.322 4.516 5.304 5.761
beta_H[13,3] 8.836 0.174 8.477 8.839 9.177
beta_H[14,3] 5.720 0.275 5.102 5.738 6.223
beta_H[15,3] 10.365 0.311 9.750 10.357 10.986
beta_H[16,3] 6.210 0.644 4.740 6.297 7.258
beta_H[1,4] 8.265 0.176 7.897 8.275 8.586
beta_H[2,4] 10.128 0.120 9.866 10.134 10.345
beta_H[3,4] 10.122 0.164 9.758 10.132 10.414
beta_H[4,4] 11.801 0.446 10.903 11.808 12.673
beta_H[5,4] 5.485 0.740 4.260 5.418 7.142
beta_H[6,4] 7.077 0.918 4.974 7.358 8.328
beta_H[7,4] 8.239 0.360 7.517 8.250 8.936
beta_H[8,4] 6.710 0.235 6.282 6.717 7.115
beta_H[9,4] 7.199 0.468 6.278 7.194 8.135
beta_H[10,4] 7.758 0.241 7.315 7.751 8.265
beta_H[11,4] 9.395 0.198 9.010 9.396 9.770
beta_H[12,4] 7.140 0.214 6.743 7.137 7.576
beta_H[13,4] 9.047 0.138 8.774 9.046 9.305
beta_H[14,4] 7.736 0.219 7.312 7.725 8.182
beta_H[15,4] 9.472 0.227 9.025 9.472 9.919
beta_H[16,4] 9.362 0.245 8.928 9.341 9.891
beta_H[1,5] 8.984 0.145 8.688 8.990 9.263
beta_H[2,5] 10.781 0.094 10.606 10.778 10.981
beta_H[3,5] 10.921 0.174 10.614 10.909 11.277
beta_H[4,5] 8.388 0.469 7.465 8.378 9.355
beta_H[5,5] 5.424 0.591 4.030 5.473 6.428
beta_H[6,5] 8.789 0.618 7.913 8.639 10.267
beta_H[7,5] 6.781 0.340 6.109 6.775 7.444
beta_H[8,5] 8.208 0.205 7.847 8.193 8.617
beta_H[9,5] 8.214 0.477 7.283 8.211 9.171
beta_H[10,5] 10.078 0.236 9.591 10.081 10.549
beta_H[11,5] 11.504 0.229 11.053 11.504 11.974
beta_H[12,5] 8.479 0.201 8.084 8.475 8.909
beta_H[13,5] 10.006 0.133 9.743 10.005 10.271
beta_H[14,5] 9.201 0.232 8.784 9.191 9.674
beta_H[15,5] 11.168 0.242 10.691 11.169 11.655
beta_H[16,5] 9.923 0.181 9.545 9.928 10.272
beta_H[1,6] 10.172 0.182 9.852 10.155 10.578
beta_H[2,6] 11.514 0.109 11.294 11.514 11.735
beta_H[3,6] 10.811 0.162 10.468 10.820 11.107
beta_H[4,6] 12.888 0.823 11.247 12.898 14.501
beta_H[5,6] 5.879 0.605 4.745 5.860 7.091
beta_H[6,6] 8.789 0.661 6.949 8.909 9.743
beta_H[7,6] 9.848 0.578 8.712 9.840 10.984
beta_H[8,6] 9.522 0.269 9.035 9.532 9.979
beta_H[9,6] 8.471 0.790 6.940 8.469 10.097
beta_H[10,6] 9.511 0.324 8.822 9.536 10.085
beta_H[11,6] 10.820 0.360 10.037 10.855 11.453
beta_H[12,6] 9.373 0.250 8.883 9.370 9.883
beta_H[13,6] 11.045 0.165 10.747 11.042 11.392
beta_H[14,6] 9.826 0.297 9.228 9.828 10.403
beta_H[15,6] 10.830 0.426 9.974 10.835 11.645
beta_H[16,6] 10.542 0.235 10.035 10.554 10.980
beta_H[1,7] 10.894 0.830 8.865 11.002 12.221
beta_H[2,7] 12.218 0.453 11.280 12.225 13.081
beta_H[3,7] 10.552 0.677 9.044 10.617 11.663
beta_H[4,7] 2.426 4.244 -5.775 2.343 11.055
beta_H[5,7] 6.417 1.853 3.053 6.378 10.360
beta_H[6,7] 9.553 2.424 4.629 9.530 15.737
beta_H[7,7] 10.580 2.866 4.929 10.619 16.211
beta_H[8,7] 10.935 0.925 9.395 10.900 12.490
beta_H[9,7] 4.417 4.082 -3.827 4.473 12.374
beta_H[10,7] 9.819 1.439 7.292 9.756 12.835
beta_H[11,7] 10.954 1.724 7.816 10.812 14.732
beta_H[12,7] 9.997 0.921 7.910 10.092 11.601
beta_H[13,7] 11.653 0.757 9.764 11.755 12.802
beta_H[14,7] 10.396 0.947 8.330 10.466 12.093
beta_H[15,7] 12.083 2.236 7.877 12.025 16.689
beta_H[16,7] 12.331 1.283 10.250 12.151 15.249
beta0_H[1] 8.538 13.352 -19.263 8.378 34.817
beta0_H[2] 10.630 6.392 -3.501 10.841 23.244
beta0_H[3] 9.622 10.607 -11.162 9.769 29.000
beta0_H[4] 9.514 182.893 -348.471 6.382 389.873
beta0_H[5] 3.990 23.995 -42.276 4.260 49.714
beta0_H[6] 6.331 50.904 -106.842 7.654 111.522
beta0_H[7] 1.330 139.531 -282.917 3.422 270.283
beta0_H[8] 6.820 24.898 -13.401 6.551 27.683
beta0_H[9] 8.098 118.552 -234.485 6.728 247.037
beta0_H[10] 9.022 32.050 -55.196 8.864 74.571
beta0_H[11] 9.213 48.539 -97.161 9.871 104.512
beta0_H[12] 6.956 10.723 -13.507 6.835 28.522
beta0_H[13] 10.069 10.630 -10.856 9.975 30.293
beta0_H[14] 6.510 11.545 -17.807 6.790 29.081
beta0_H[15] 7.591 108.521 -216.835 9.428 229.258
beta0_H[16] 8.433 26.038 -43.629 8.224 63.222